What are mathematical limits?

A mathematical limit is like watching something get closer and closer to a certain point, without actually reaching it, imagine your favorite cookie getting nearer and nearer to your mouth, but you're still waiting for the final bite!

Think of a limit as a race between two friends: one is running towards a finish line, and the other is standing at that finish line, just watching. No matter how close the runner gets, they never actually touch the finish line, but we can still say they approached it.

Let’s say you're eating cookies one by one: 1 cookie, then 2, then 3… each time, you’re getting closer to finishing all of them. If there are 10 cookies total, the number of cookies left gets smaller and smaller, like this:

• After 1 cookie: 9 left
• After 2 cookies: 8 left
• …
• After 9 cookies: 1 left

Even though you never actually finish all the cookies at once, you can still say that the number of cookies approaches zero. That’s a limit, it's about what happens as something gets closer and closer to a value, even if it never quite gets there!